Dispersion for Schrödinger Operators with One-gap Periodic Potentials on R^1

Details Dispersion for Schrödinger Operators with One-gap Periodic Potentials on R^1 Dispersion for Schrödinger Operators with One-gap Periodic Potentials on R^1

2004-10-31

arxiv.org/abs/math-ph/0411002v1

Physics

Mathematical Physics

23 pages

Scientific paper

We prove $t^{- \frac 14}-$decay for the solutions of the 1-dim Schrodinger
equation with a one-gap periodic potential as $t \to +\infty $. Generically,
one has $t^{- \frac 13}$-decay and this decay is optimal. Our approach is to
analyze the stationary phase in the Schr\"odinger evolution as an integral
operator.

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